Module 32. Game Theory. Module Objectives. Module Outline. I. Games Oligopolists Play


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1 Module 32 Game Theory Module Objectives Students will learn in this module: How our understanding of oligopoly can be enhanced by using game theory. The concept of the prisoners dilemma. How repeated interactions among oligopolists can result in collusion in the absence of any formal agreement. Module Outline I. Games Oligopolists Play A. Definition: The study of behavior in situations of interdependence is known as game theory. B. The prisoners dilemma 1. Definition: The reward received by a player in a game, such as the profits earned by an oligopolist, is that player s payoff. 2. Definition: A payoff matrix shows how the payoff to each of the participants in a twoplayer game depends on the actions of both. This is illustrated in text Figure 321, shown on the next page. 176
2 module 32 game theory 177 A Payoff Matrix Ajinomoto Produce 30 million pounds Produce 40 million pounds Produce 30 million pounds $180 million $180 million $200 million $150 million ADM Produce 40 million pounds $200 million $150 million $160 million $160 million a. In a prisoners dilemma game, each player has an incentive, regardless of what the other player does, to cheat, to take an action that benefits it at the other s expense. b. When both players in the prisoners dilemma cheat, both are worse off than they would have been if neither had cheated. c. Definition: An action is a dominant strategy when it is a player s best action regardless of the action taken by the other player. d. Definition: A Nash equilibrium, also known as a noncooperative equilibrium, is the result when each player in a game chooses the action that maximizes his or her payoff given the actions of the other players, ignoring the effects of that action on the payoffs received by those other players. C. Overcoming the prisoners dilemma: Repeated interaction and tacit collusion 1. Oligopolists in the real world play repeated games. 2. Definition: A firm engages in strategic behavior when it attempts to influence the future behavior of other firms. 3. Definition: A strategy of tit for tat involves playing cooperatively at first, then doing whatever the other player did in the previous period. Doing this, a firm can punish another firm for cheating. 4. Definition: When firms limit production and raise prices in a way that raises each others profits, even though they have not made any formal agreement, they are engaged in tacit collusion. 5. When oligopolists expect to compete with each other over an extended period, each individual firm will often find it in its own best interests to help other firms in the industry, and so there will be tacit collusion.
3 178 module 32 game theory Teaching Tips Games Oligopolists Play Creating Student Interest Tell students that you are going to give them a pop quiz. The only question on the quiz is, What grade would you like to receive on this quiz? The two permitted answers are A or C (though those are not the only possible grades they may receive). Then explain that the grade they will actually receive on the quiz depends on their answer and the answer of another student in the class. (Each student will be randomly paired with another student. If there is an odd number of students in the class, the remaining student will be paired with the instructor.) Tell the students that the grade assigned for the quiz will be determined by the following payoff matrix: A You C You: F You: F A Other Student C Them: F You: A Them: A You: C Them: F Them: A Have students write their name and their choice (A or C) on a small slip of paper and collect all the decisions and put them in a hat. Draw two names at a time and inform the students what grade they receive, based on the payoff matrix. After assigning all the grades, ask the students what they think. You will likely get comments like It s not fair! You can also repeat the exercise and/or change the payoffs. Presenting the Material Use the payoff matrix below. In this game, there are two airlines, Sky World and Bay City Airlines, and they have the choice of pricing high or low. Each company s profit depends on how the other company responds to its pricing strategy. If both firms collude and agree on a high price, they each earn $30 in If one prices low and the other prices high, the lowprice firm earns $50 (grabbing market share), while the high price firm earns only $4. Because of the risk of retaliation, the likely outcome is that both firms will price low and earn only $10 each. The dominant strategy in this game is to choose a low price.
4 module 32 game theory 179 Sky World High Low High Bay City Low Students should be able to grasp the concept of a dominant strategy from the matrix provided. They should also be able to understand why a firm would have an incentive to break an agreement to collude, based on the example from the previous section. These are all oneperiod examples. Now that students have mastered oneperiod games, introduce the concept of a repeated game. Discuss tit for tat and explain that tacit collusion is a likely outcome. Case Studies in the Text Economics in Action Prisoners of the Arms Race This EIA looks at the arms race between World War II and the late 1980s as an example of the application of game theory. Activities Tit for Tat? (30 45 minutes) Organize students into teams of three, with each team representing a specific oligopoly industry. Each student represents a specific company within the oligopoly. Make this clear by standing by one team and indicating that one student may play the role of Kellogg s, the second Quaker Oats, and the third student General Mills. The goal of each company is to maximize profits for their corporation. Explain that during this experiment, each firm must decide whether to choose a high price for their product (H = $8) or a low price (L = $6). (In this game, oligopolists are competing on price alone, not on quantities.) If a student is operating as the price leader, she will signal a high price by thumbs up and a low price by thumbs down. Before the experiment begins, distribute the following chart for students to fill out.
5 180 module 32 game theory Prices Total cost (possible Total sales Total ($110 fixed outcomes of in the Firm s sales revenue and each round) market Price (quantity) (P x Q) $2 variable) Profit HHH 60,60, H = $8 HHL 20,20, H = $8 L = $6 HLL 10,100, H = $8 L = $6 LLL 216 L = $6 72,72,72 During the game, students track their pricing and profits with the form below: Profit or Loss Statement form (extend this form to show 15 rounds): Industry situation Your firm s price Round (HHH,HHL,HLL,LLL) (H or L) Profit Loss Tell students that any verbal discussion on pricing strategy during the game will be punished under antitrust laws: a team can be thrown out into the hall. Optional: Remind students that the most profitable strategy for the industry as a whole is to collude. To start the experiment, ask each team to choose a price leader for the first round; the student taking this role changes each round. Ask the price leader to choose a high or low price and signal to the team his or her choice. Then have the two other students choose their prices and secretly record them on the firm s profit sheet, covering their prices with their hands. Now it is time for them to reveal their pricing decisions to the industry. The oligopoly determines the outcome: HHH, HHL, HLL, LLL, etc. Then each firm records its individual profit or loss for this first round. Teams continue this process until they have played all 15 rounds: The new price leader shows the choice of his or her firm s price, and the two other firms secretly respond. The two firms show their choice, the oligopoly determines the outcome, and individual firms record their profit or loss for that round. Observe the teams during the game to see if any are able to achieve tacit collusion and agree on a high price. Because leading with a high price risks rivals undercutting the price, the least risky strategy is to lead with a low price. Students tend to use a tit for tat strategy in this game.
6 module 32 game theory 181 To Collude or Not? (5 10 minutes) Use the payoff matrix shown previously for the two airlines to play the following game. Pair students and tell them that each student in a pair represents an airline in a duopoly. On the count of three, each student chooses a high or a low price by signaling thumbs up or thumbs down. Students then record their profits based on the payoff matrix. Round Your price Your payoff Profit Debrief the game by pointing out that the dominant strategy in this game is to choose a low price. Oligopoly (10 minutes) The Classroom Expernomics website has a variety of classroom experiments that can be used to teach about oligopoly. Go to html and type in oligopoly, collusion or cartel to find interesting activities.
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